3m^2+9m+1=10

Solution for 3m^2+9m+1=10 equation:

Simplifying
3m2 + 9m + 1 = 10

Reorder the terms:
1 + 9m + 3m2 = 10

Solving
1 + 9m + 3m2 = 10

Solving for variable 'm'.

Reorder the terms:
1 + -10 + 9m + 3m2 = 10 + -10

Combine like terms: 1 + -10 = -9
-9 + 9m + 3m2 = 10 + -10

Combine like terms: 10 + -10 = 0
-9 + 9m + 3m2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 3m + m2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-3 + 3m + m2)' equal to zero and attempt to solve:

Simplifying
-3 + 3m + m2 = 0

Solving
-3 + 3m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 3m + 3 + m2 = 0 + 3

Reorder the terms:
-3 + 3 + 3m + m2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 3m + m2 = 0 + 3
3m + m2 = 0 + 3

Combine like terms: 0 + 3 = 3
3m + m2 = 3

The m term is 3m.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3m + 2.25 + m2 = 3 + 2.25

Reorder the terms:
2.25 + 3m + m2 = 3 + 2.25

Combine like terms: 3 + 2.25 = 5.25
2.25 + 3m + m2 = 5.25

Factor a perfect square on the left side:
(m + 1.5)(m + 1.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(m + 1.5) equal to 2.291287847 and -2.291287847.

Subproblem 1
m + 1.5 = 2.291287847

Simplifying
m + 1.5 = 2.291287847

Reorder the terms:
1.5 + m = 2.291287847

Solving
1.5 + m = 2.291287847

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + m = 2.291287847 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + m = 2.291287847 + -1.5
m = 2.291287847 + -1.5

Combine like terms: 2.291287847 + -1.5 = 0.791287847
m = 0.791287847

Simplifying
m = 0.791287847

Subproblem 2
m + 1.5 = -2.291287847

Simplifying
m + 1.5 = -2.291287847

Reorder the terms:
1.5 + m = -2.291287847

Solving
1.5 + m = -2.291287847

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + m = -2.291287847 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + m = -2.291287847 + -1.5
m = -2.291287847 + -1.5

Combine like terms: -2.291287847 + -1.5 = -3.791287847
m = -3.791287847

Simplifying
m = -3.791287847

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.791287847, -3.791287847}
Solution
m = {0.791287847, -3.791287847}